Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11126 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #121 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| socle | C22×C71 | #390 |
| prime radical | C22×#41×C71 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C23×C4×C71 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 107 points:
(2,4)(5,6)(7,17)(8,22,26,13)(9,16)(10,14)(11,15)(12,19)(18,33,35,30)(20,28)(21,29)(23,36,34,27)(24,31,25,32)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,2,3,4)(5,7,9,19,11,21,10,20)(6,12,14,17,15,28,16,29)(8,23,24,18,26,34,25,35)(13,30,31,27,22,33,32,36);(5,8)(6,13)(7,18)(9,25)(10,24)(11,26)(12,27)(14,32)(15,22)(16,31)(17,30)(19,23)(20,34)(21,35)(28,36)(29,33)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4114);